Various audio coding systems have been developed in the prior art for compressing the amount of data needed to represent a multichannel audio signal carrying three or more channels. One such known coding system is the MPEG Surround System standardized by the Moving Picture Experts Group (MPEG) (for example, refer to ISO/IEC 23003-1). In the MPEG Surround System, a plurality of channel signals are downmixed to generate spatial information and a main signal representing the main component of each original channel signal, and this main signal and the spatial information are encoded. Further, in this coding system, a residual signal representing a component orthogonal to the main signal is also computed, and this residual signal may also be encoded.
The main signal and the residual signal are each obtained by first transforming the downmix signal into a time domain signal and then transforming it into a frequency domain signal by a modified discrete cosine transform (MDCT). Of these two signals, the main signal once transformed into the time domain signal is further transformed into QMF coefficients representing a time-frequency domain signal by using a quadrature mirror filter (QMF), because upmixing is performed using the spatial information when decoding. Therefore, the residual signal in the frequency domain is also transformed into QMF coefficients in the time-frequency domain so that the residual signal can be used when upmixing.